Ohio State University Algebraic Geometry Seminar


Ohio State University Algebraic Geometry Seminar Year 2024-2025 Time: Tuesdays 10:20-11:15am Location: MW 154 (in person) or Zoom (virtual, email the organizers for the Zoom coordinates)

Schedule of talks:


TIME	SPEAKER	TITLE
August 27 Tue, 10:20am	Richard Haburcak (OSU)	Distinguishing Brill-Noether loci
September 3 Tue, 10:20am	William Newman (OSU)	Chow Groups of Moduli Spaces Via Higher Chow Groups
September 8-11 time TBD room TBD	Michel Talagrand (CNRS)	Special lecture by Michel Talagrand (Abel Prize 2024 winner)
September 17 Tue, 10:20am	Desmond Coles (UT Austin)	Spherical tropicalization
September 24 Tue, 10:20am	TBA ()	TBA
October 1 Tue, 10:20am	Hsian-Hua Tseng (OSU)	Elliptic curves and Hilbert schemes of points
October 8 Tue, 10:20am	TBA ()	TBA
October 15 Tue, 10:20am	Linda Chen (Swarthmore)	TBA
October 22 Tue, 10:20am	Linus Setiabrata (U. Chicago)	TBA
October 29 Tue, 10:20am	TBA ()	TBA
November 4-6 4:15pm room TBD	Alexei Borodin (MIT)	Rado Lecture Series 2024
November 12 Tue, 10:20am	Ian Cavey (UIUC)	TBA
November 19 Tue, 10:20am	TBA ()	TBA
November 26 Tue, 10:20am	(no seminar)	Thanksgiving week
December 3 Tue, 10:20am	TBA ()	TBA
January 7 Tue, 10:20am	TBA ( )	TBA
January 14 Tue, 10:20am	TBA ( )	TBA
January 21 Tue, 10:20am	TBA ( )	TBA
January 28 Tue, 10:20am	TBA ( )	TBA
February 4 Tue, 10:20am	TBA ( )	TBA
February 11 Tue, 10:20am	TBA ( )	TBA
February 18 Tue, 10:20am	TBA ( )	TBA
February 25 Tue, 10:20am	TBA ( )	TBA
March 4 Tue, 10:20am	TBA ()	TBA
March 11 Tue, 10:20am	(no seminar) ()	Spring Break (no seminar)
March 18 Tue, 10:20am	TBA ()	TBA
March 25 Tue, 10:20am	TBA ()	TBA
April 1 Tue, 10:20am	TBA ()	TBA
April 8 Tue, 10:20am	TBA ()	TBA
April 15 Tue, 10:20am	TBA ()	TBA
April 22 Tue, 10:20am	TBA ()	TBA

See also the Arithmetic Geometry Seminar

Abstracts

(Haburcak): Classical Brill-Noether theory studies linear systems on a general curve in the moduli space M_g of algebraic curves of genus g. A refined Brill-Noether theory studies the linear systems on curves with a given Brill-Noether special linear system. As a first step, one would like to understand the stratification of M_g by Brill-Noether loci, which parameterize curves with a particular projective embedding. We'll discuss recent progress on distinguishing Brill-Noether loci and the recent resolution of the Maximal Brill-Noether loci conjecture, identifying the maximal elements of the stratification by Brill-Noether loci. This is based on joint work with Asher Auel, Andrei Bud, Andreas Leopold Knutsen, and Hannah Larson.

(Newman): One can use Bloch's higher Chow groups to compute the usual Chow groups of moduli spaces. This involves first computing the necessary higher Chow groups, and then computing the connecting homomorphism of the localization exact sequence. I will explain general techniques for performing these computations and give examples for the integral Chow groups of moduli spaces of genus 1 curves.

(Coles): In recent decades tropical geometry, the study of algebraic varieties by constructing an associated 'combinatorial shadow', has proven to be a fruitful toolkit in many areas of algebraic geometry. The starting point for constructing these shadows has often been the tropicalization of toric varieties. In this talk I will explain how tropicalization can be extended to a larger class of varieties, spherical varieties, and I will also discuss the connection with Berkovich geometry.

(Tseng): Hilbert schemes of points on the affine plane are arguably the moduli spaces of sheaves with the richest known structures. The Deligne-Mumford moduli spaces of stable curves are by far the most studied moduli spaces of varieties in algebraic geometry. Stable maps provide a system of correspondences between these moduli spaces. In particular, one can construct (cycle) classes on moduli spaces of curves from classes on Hilbert schemes. In this talk, we discuss a numerical study of these classes in the genus 1 case.

(Setiabrata): TBD

(Cavey): TBD

(Chen): TBD